Question

A right triangle has acute angles measuring 2x+6
degrees and 3x−26
degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.(4 points)

make the answer of how you got it sound like a 12 y old wrote it

Answer 1

To find the missing angles in the triangle, we can use the Triangle Angle Sum Theorem. This theorem says that all the angles in a triangle add up to 180 degrees.

We have two angles given: one is \(2x + 6\) degrees and the other is \(3x - 26\) degrees. The third angle, which is the right angle, measures 90 degrees because it's a right triangle.

So, our equation looks like this:

\[
(2x + 6) + (3x - 26) + 90 = 180
\]

Now, we can simplify this step-by-step:

1. Combine the angles:
\[
2x + 6 + 3x - 26 + 90 = 180
\]

2. Start by combining like terms:
- For the \(x\) terms: \(2x + 3x = 5x\)
- For the constant terms: \(6 - 26 + 90 = 70\)

So it becomes:
\[
5x + 70 = 180
\]

3. Now, we want to get \(5x\) by itself. We can do that by subtracting 70 from both sides:
\[
5x = 180 - 70
\]
This simplifies to:
\[
5x = 110
\]

4. Next, divide both sides by 5 to find \(x\):
\[
x = \frac{110}{5} = 22
\]

Now that we know \(x\), we can find the actual angles:

1. For the first angle, \(2x + 6\):
\[
2(22) + 6 = 44 + 6 = 50
\]
So, the first angle is 50 degrees.

2. For the second angle, \(3x - 26\):
\[
3(22) - 26 = 66 - 26 = 40
\]
So, the second angle is 40 degrees.

Finally, we can summarize the angles of the triangle:
- One angle is 90 degrees (the right angle),
- Another angle is 50 degrees,
- And the last angle is 40 degrees.

In total, the three angles are 90°, 50°, and 40°. And they all add up to 180 degrees, just like the Triangle Angle Sum Theorem tells us!